Correspondence Between 3D Shapes Based on Improved Functional Map

We propose a shape matching algorithm based on an improved functional map in order to calculate correspondence between two given 3D non-rigid shapes, in which shape correspondence can be represented as a mapping function of mixed transformation matrix B and calibration matrix P of basis functions. First, Laplace matrix is calculated and a new matrix is constructed as basis matrix of function space by using eigenvectors of Laplace matrix after eigen-decomposition. Then, a calibration algorithm based on statistical covariance is proposed to calculate the matrix P that is used to calibrate basis matrices of function space of two shapes. Finally, the matrix B is optimized by an improved ICP(Iterative Closest Point) algorithm in order to calculate shape correspondence with the matrix P. Experimental results show that the proposed algorithm avoids excessive initial conditions, obtains accurate shape correspondence and significantly solves symmetry ambiguities of 3D shapes during matching process.